Tayyebi and Jenerette found that NDVI and LST were negatively correlated across coastal, inland, and desert zones:
Tayyebi, Amin, and Darrel G Jenerette. “Increases in the Climate Change Adaption Effectiveness and Availability of Vegetation across a Coastal to Desert Climate Gradient in Metropolitan Los Angeles, CA, USA.” Science of The Total Environment 548-549: 60–71.